Đáp án+Giải thích các bước giải:
`x- (x-3)/((sqrtx -2)-1)` `(ĐK: x ge 2,x ne 3)`
`= x- ((x-3)(sqrt(x-2)-1))/((sqrt(x-2)-1)(sqrt(x-2)-1))`
`= x -((x-3)(sqrt(x-2)-1))/(x-2-1)`
`= x-(sqrt(x-2)+1)`
`= x - sqrt(x-2) -1`
`= x - sqrt(x-2) -2+1`
`= x - sqrt(x-2) -2 + 1/4 + 3/4`
`= ( sqrt(x-2) -1/2)^2 + 3/4 ge 3/4`
Vậy `min = 3/4`
Dấu `=` xảy ra khi `sqrt(x-2)-1/2 =0`
`<=> sqrt(x-2) = 1/2`
`<=> x-2 = 1/4`
`<=> x = 9/4`
